MMSI – SATURDAY SESSION with Mr. Flynn

Describing patterns and departures from patterns (20%–30% of exam) Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries.

A. Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stem&leaf, histogram, cumulative frequency plot) 1. Center and spread 2. Clusters and gaps 3. Outliers and other unusual features 4. Shape B. Summarizing distributions of univariate data 1. Measuring center: median, mean 2. Measuring spread: range, interquartile range, standard deviation 3. Measuring position: quartiles, percentiles, standardized scores (z-scores) 4. Using boxplots 5. The effect of changing units on summary measures

C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) 1. Comparing center and spread: within group, between group variation 2. Comparing clusters and gaps 3. Comparing outliers and other unusual features 4. Comparing shapes D. Exploring bivariate data 1. Analyzing patterns in scatterplots 2. Correlation and linearity 3. Least-squares regression line 4. Residual plots, outliers and influential points 5. Transformations to achieve linearity: logarithmic and power transformations Yates Chapter 3 E. Exploring categorical data 1. Frequency tables and bar charts 2. Marginal and joint frequencies for two-way tables 3. Conditional relative frequencies and association 4. Comparing distributions using bar charts Test #1 at the end of this week

CATEGORICAL DISPLAYSQUANTITATIVE DISPLAYS Pie Charts Bar Graphs Stemplots Histograms Boxplots

Displaying Data Is it categorical or contain labels? Pie ChartsBar Graphs Is it numerical or contain intervals of values? Stemplots (Stem & Leaf Plots) Histograms 1. Comparing parts to the whole 2. Must contain all possibilities to total 100% 3. Model for problem solving 1.Comparing most to least among several categories 1. Comparing categories of 10’s or 100’s 2. Data must be retrieved later 3. Median or mode is best measure of center 4. Back to back frequency comparisons 1. Comparing intervals of chosen size 2. Individual data is not vital 3. Mean or Median is best measure of center 4. Frequency or Probability given Describing patterns and departures from patterns (20%–30%) Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries.

What possible graphs can you make from these data sets? Make one then! RecyclablesStudent gradesStudent earnings# of meatballsChicks Glass 6%73, 81, 85, 90,$ students5, 6, 6, 5, 7, 6,¼ Blonde Paper 37%65, 100, 82, 85$ , 5, 5, 6, 5, 5, 2/3 Black Plastic 11%47, 91, 91, 83,$ , 7, 7, 6, 5, 61/12 Brown Wood 5%77, 81, 78, 88$ Aluminum13%over $40 3 Other 4%

Patterns Shape Center Spread Deviations from Patterns (Influential Points) Shift of center but Major shift of not great influence both center and on spread spread – outlier Gaps and clusters pockets of values or missing value suggesting bimodal or skewness When examining distributions we are looking for two main things: Patterns & Deviations from Patterns

Measuring Center A. Mean – for large data sets, uniform, symmetrical, normal-ish, few extremes B. Mode – for small data sets, skewed, some extreme values but not outliers C. Median – for small to moderately large data sets, symmetrical, skewed, noticeable extreme values, possible outliers

Measuring Spread A. Standard Deviation – average distance to the mean – use with mean B. Range – distance between the extremes – use with the mode C. The IQR – range of middle 50% of values – use with the median

Addition/Subtraction shifts D. Enter the following list into your calculator: 12, 15, 18, 10, 14, 12, 10, 16, 15, 9, 11, 12, 18 Find the three measures of center and spread Now add the month of your birthday to each value; store in another list Next subtract the number of family members you have to each value; store in another list What are the centers and spread now for two new lists? Scalar Transformations D. Enter the following list into your calculator: 12, 15, 18, 10, 14, 12, 10, 16, 15, 9, 11, 12, 18 Find the three measures of center and spread Now multiple the month of your birthday to each value; store in another list Next divide the number of cars your family has into each value; store in another list What are the centers and spread now for two new lists? Notice anything ? Could you write a conjecture?

Dot plot? Data may be expressed on a number line. Cannot be accurately done with large sets of data or with non-integers; think discrete random variables.. Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries What is an ogive? Data may be expressed using a single line. An ogive (a cumulative line graph) is best used when you want to display the total at any given time. Very similar to the normal distribution plot on your calculator (you know the one you never use) Box plot? Data may be expressed on a number line. Must find the 5 number summary...may or may not include outliers…good for non-symmetrical data sets

Warm Up: Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries

Make an ogive of a set of quantitative data Practice Problem p. 64 #1.14b

Make a rough histogram from these ogives

What is a boxplot?

Why Use Boxplots? Boxplots help us to compare distributions side by side They also allow us to see the shape of the distribution Five Number Summary & Boxplots Minimum 1 st Quartile Median 3 rd Quartile Maximum min Q 1 Q 2 Q 3 max The Interquartile Range IQR Q 3 – Q 1 An observation may be an outlier if it falls more than 1.5xIQR above Q 3 or below Q 1

Warm Up:

Use the fish tank method to make a rough histogram of each boxplot.

Assessing Shape A. Look for overall patterns & for major deviations from patterns B. Determine whether or not the distribution is roughly symmetric, distinctly skewed, or neither. Look for modes C. Describe the overall pattern by giving numerical measures of center, spread and a verbal description of shape.

Inspecting Distributions (Quantitative Variables) D. Decide which measures of center & spread are more appropriate: For Symmetric Distributions & No Outliers the mean & standard deviation For Skewed Distributions or Strong Outliers the five-number summary E. Recognize Outliers IQR x 1.5

Data: Organize & examine Data Graphs: Construct the appropriate graphical displays Numerical Summaries: Calculate relevant summary statistics Interpretation: Discuss what the data, graphs & numerical summaries tell you in the context of the problem. Answer the Question! POP QUIZ! EXIT SLIP!